EXOTIC BARYONS IN TOPOLOGICAL SOLITON MODELS. V.B.Kopeliovich Institute for Nuclear Research of RAS, Moscow, 117312 The status and properties of pentaquarks discovered recently are discussed within topological soliton and simplistic quark model. 1 Discovery of pentaquarks One of striking events in elementary particle physics after latest Quarks conference was discovery of baryon resonances with unusual properties (end of 2002 - 2004): + Θ (1540); strangeness S = +1, isospin I = 0 (most likely), width ΓΘ < 10 Mev, seen by different collaborations in Japan, Russia, USA, FRG, CERN; −− Ξ3=2 (1862), S = 2 , I = 3=2 (?), Γ < 18 Mev observed by NA49 Collab. at CERN; 0 − P Θc(3099), charm C = 1, Γ < 15 Mev seen by H1 Collab., DESY. Spin-parity J of these states is not measured− yet. These states are manifestly exotic because they cannot be made of 3 valence quarks only. There are different possibilities to have exotic baryon states: a) positive strangeness S > 0 (or negative charm C < 0, or positive beauty), since s-quark has S = 1 and c-quark C = +1, b) large (in modulus)− negative strangeness S < 3B, B - baryon number; similar for charm or beauty, − c) large enough isospin I > (3B + S)=2 , if 3B S 0, or charge Q > 2B + S or − ≤ ≤ Q < B in view of Gell-Mann - Nishijima relation Q = I3 + Y=2. − + The pentaquarks Θ (1540) and Θc(3099), if it is confirmed, are just of the type a), the possibility b) is difficult to be realized in practice, since large negative strangeness of produced baryon should be balanced by corresponding amount of pos- −− itively strange kaons. The state Ξ3=2 is of the type c). The minimal quark contents + −− 0 of these states are: Θ = (dduus¯); Ξ = (ssddu¯); Θc = (dduuc¯), and by this reason they are called pentaquarks. Chronology of pentaquarks discovery. Θ+; S = +1 baryon was observed first at SPring-8 installation (RCNP, Japan)[1] in reaction γ12C K+n+:::. The reported mass is 1540 10 Mev and width Γ < 25 Mev, confidence level!(CL) 4:6σ. Soon after this and independently DIANA collaboration at ITEP, Moscow [2] observed Θ+ in interactions of K+ in Xe bubble chamber. The mass of the bump in K0p invariant mass distribution is 1539 2 Mev; Γ < 9 Mev, confidence level a bit lower, about 4:4σ. Confirmation of thisresult came also from several other experiments [3, 4, 5, 6, 7, 8, 9] mostly in reactions of photo-(electro)- production. The CLAS Collaboration [10] provided recently evidence for two states in Θ-region of the K+n invariant mass distribution at 1523 5 Mev and 1573 5 Mev. The nonobservation of Θ+ in old kaon-nucleon scattering data provided restric- tion on the width of this state. Phase shift analysis of KN-scattering in the energy interval 1520 1560 Mev gave a restriction Γ < 1 Mev [11]. Later analysis of total cross sections −of kaon-deuteron interactions allowed to get the estimate for the width of Θ+: Γ 0:9 0:2 Mev [12]. ' The doubly strange cascade hyperon Ξ3=2; S = 2, probably with isospin I = 3=2 is observed in one experiment at CERN, only, −in proton-proton collisions at 17Gev[13]. The mass of resonance in Ξ−π− and Ξ¯+π+ systems is 1862 2 Mev and mass of resonance in Ξ−π+; Ξ¯+π− systems is 1864 5 Mev; width Γ <18 Mev, and CL = 4:0σ. The fact makes this result more reliablethat resonance Ξ−− was observed in antibaryon channel as well. However, this resonance is not confirmed by HERA-B, ZEUS, CDF, WA-89 collaborations (see e.g. [14]), although there is no direct contra- diction with NA49 experiment: upper bounds on the production cross sections of Ξ3=2 are obtained in this way. 0 The anticharmed pentaquark Θc; C = 1 was observed at H1, HERA, Ger- many, in ep collisions. The mass of resonance in− D∗−p; D∗+p¯ systems is 3099 3 5 Mev; Γ < 15 Mev; CL = 6:2σ. ZEUS collaboration at HERA [16] did notcon- 0 firm the existence of Θc with this value of mass, and this seems to be already serious contradiction, see again [14]. There is also some evidence for existence of other baryon states, probably exotic, 0 e.g. nonstrange state decaying into nucleon and two pions [17] or resonance in ΛKS system with mass 1734 6 Mev; Γ < 6 Mev at CL = (3 6)σ which is N ∗0 or Ξ∗ , − 1=2 observed by STAR collaboration at RHIC [18] in reaction Au+Au at psNN 200 Gev. Already after the Quarks-04 conference the negative results on Θ+ observ∼ ation have been reported by several groups. If high statistics experiments will not confirm existence of Θ+, it would be interesting then to understand why about 10 different ex- periments, although each of them with not high statistics, using different installations and incident particles, provided similar positive results. Information about status of higher statistics experiments performed or to be performed at JLAB (CLAS Collab.) can be found in [19]. 2 Early predictions From theoretical point of view the existence of such exotic states by itself was not unexpected. Such states have been discussed first within MIT quark-bag model [20]. The mass of these states was found considerably higher than that reported now: MΘ P − ' 1700 Mev; J = 1=2 . These studies were continued by other authors [21]: MΘ 1900 Mev, J P = 1=2− and [22]. From analysis of existed that time data on KN' interactions the estimate was obtained in [23] MΘ 1705 Mev (I = 0); 1780 Mev (I = 1) with very large width. ' In the context of chiral soliton model the 10¯ and 27 -plets of exotic baryons were mentioned first in [24], without any massfestimates,g f hogwever. Rough estimate within the "toy" model, M10¯ M8 600 Mev, was made a year later in [25]. A resonance-like behaviour of KN− scattering' phase shift in Θ channel was obtained in [26] in a version of Skyrme model (in the limit MK = Mπ). Numerical estimate MΘ 1530 Mev was obtained by M.Praszalowicz [27], but it was no serious grounds for this' since mass splittings within octet and decuplet of baryons was not described here satisfactorily ("accidental" prediction). Extension of quantization condition [28] to "exotic" case was made in [29] where masses of exotic baryonic systems (B arbitrary, Nc = 3) were estimated as function of the number of additional quark-antiquark pairs, or "exoticness number m": ∆E 2 ∼ m=ΘK; m =ΘK. But here it was no mass splittings estimates inside of multiplets, no discussion of masses of particular baryons. First calculation with configuration mixing due to flavor symmetry breaking (mK = mπ) was made in [30] where mass splittings within the octet and decuplet of baryons6 were well described, and estimate obtained M 1660 Mev. "Strange" or Θ ' kaonic inertia ΘK was underestimated in this work, as it is clear now. The estimate M 1530 Mev, coinciding with [27], and first estimate of the Θ ' width, ΓΘ < 30 Mev were made 5 years later in [31]. It was "a luck", as stated much later by same authors (hep-ph/0404212): mass splitting inside of 10¯ was obtained greater than for decuplet of baryons, 540 Mev, and it was supposed that resonance N ∗(1710) 10¯ , i.e. it is the nonstrange component of antidecuplet. The above mass value was2a fresultg of subtraction, 1530 = 1710 540=3. [31] is instructive example − of a paper which, strictly speaking, is not quite correct, but being in right direction, stimulated successful searches for Θ+ in RCNP (Japan) and ITEP (Russia). Skyrme-type model with vibrational modes included was studied first in [32] with a result MΘ 1570 Mev; ΓΘ 70 Mev. A mistake (or misprint?) in paper's [31] width estimate'was noted here. ∼ Developements after Θ+ discovery. After discovery of pentaquarks there appeared big amount of papers on this subect which develop theoretical ideas in different directions: within chiral soliton models [33, 34] and many other, phenomenological correlated quark models [35, 36, 37] and other, QCD sum rules [38], by means of lattice calculations [39], etc. It is not possible to describe all of them within restricted framework of this talk (reviews of that topic from different sides can be found, e.g. in [42, 46]). Quite sound criticism concerning chiral soliton models was developed in [40, 41], but it should be kept in mind that the drawbacks of soliton approach should be compared with uncertainces and drawbacks of other models. There is no regular way of solving relativistic many-body problem of finding bound states or resonances in 3-,5-, etc. quark system, and the chiral soliton approach, in spite of its drawbacks, provides a way to circumwent some of difficulties. The correlated quark models, diquark-triquark model [35], or diquark- diquark-antiquark model [36], being interesting and predictive, contain good amount of phenomenological guess. 3 Topological soliton model In spite of some uncertainties and discrepances between different papers, the chiral soliton approach provided predictions for the masses of exotic states near the value observed later, considerably more near than quark or quark-bag models. Here I will be restricted with this model, mainly. Situation is somewhat paradoxical: it is easier to estimate masses of exotic states within chiral soliton models, whereas interpretation is more convenient in terms of simplistic quark model. In topological (chiral) soliton models the baryons and baryonic systems appear as classical configurations of chiral ("pionic" in simplest SU(2) version) fields which are characterized by the topological or winding number identified with the baryon number of the system [43].